Dividend approach and level consistency for the Derks and Peters value

Different from the potential approach of Hart and Mas-Colell (1989), we provide the dividend approach to multi-choice games. Also, we define the level-reduced game by reducing the number of the activity levels and define related consistency on multi-choice games.

Value, complement reduction and interval TU games

In the framework of interval transferable-utility (TU) games, we introduce a generalization of the equal allocation of nonseparable cost (EANSC). Further, we extend the reduced game introduced by Moulin (1985) to interval TU games. By applying this extended reduction, two axiomatizations of this extended EANSC are proposed.Interval TU games, the equal allocation of nonseparable cost, reduced game.

Consistency and the core for fuzzy non-transferable-utility games

Different from the works of Hwang (2007), we provide two extensions of the reduced games introduced by Moulin (1985) and Voorneveld and van den Nouweland (1998) on fuzzy non-transferable-utility (NTU) games, respectively. Based on the reduced games, we provide an axiomatization of the core and show that the technique of the proof in Tadenuma (1992) can not be applied to the core in the context of fuzzy NTU games.